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2 years ago

What is the complete factorization of the polynomial below

Mathematics

1 answer:

DerKrebs [107]2 years ago

7 0

Answer:

$a. \ (x-2)(x+i)(x-i)$

Step-by-step explanation:

First of all let's notice that $(x-i)(x-i)=(x-i)^2 = x^2+2xi-1 \in \mathbb{C}$ while our original polynomial is real. So we can rule out the even options B and D. At this point, if the polynomial has a factor of $(x-\alpha)$ it means tha $\alpha$ is a zero of the polynomial. Let's check both 2 (for option a) and -2 (for option c)

$p(2)=2^3-2(2)^2+2-2= 8-8+2-2=0$

$p(-2)= (-2)^3-2(-2)^2+(-2)-2=-8-8-2-2=-20$

At this point 2 is a zero, and our final factoring is a $(x-2)(x+i)(x-i)$

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Sekhar gives a quarter of his sweets to Renu and then gives 5 sweets to Raji. He has

Feliz [49]

Answer:

16 sweets

Step-by-step explanation:

Number of sweet that Sekhar had = x

Sweets given to Renu = (1/4) of x = $\frac{1}{4}x$

Sweets given to Raji = 5

Remaining sweets = 7

$x = \frac{1}{4}x +5 + 7\\\\x -\frac{1}{4}x = 12\\\\\frac{4*x}{1*4}x-\frac{1}{4}x = 12\\\\\frac{4x}{4}-\frac{1}{4}x= 12\\\\\frac{3x}{4}=12\\\\x = 12*\frac{4}{3}\\\\x=4*4\\\\x=16$

6 0

2 years ago

What is the volume of the rectangular prism?

Mashcka [7]

Answer:

96 cubic inches

Step-by-step explanation:

8x3=24=area x4 = 96 = volume

5 0

3 years ago

How do you do this question?

Ksivusya [100]

Answer:

V = (About) 22.2, Graph = First graph/Graph in the attachment

Step-by-step explanation:

Remember that in all these cases, we have a specified method to use, the washer method, disk method, and the cylindrical shell method. Keep in mind that the washer and disk method are one in the same, but I feel that the disk method is better as it avoids splitting the integral into two, and rewriting the curves. Here we will go with the disk method.

$\mathrm{V\:=\:\pi \int _a^b\left(r\right)^2dy\:},\\\mathrm{V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy}$

The plus 1 in '1 + 2/x' is shifting this graph up from where it is rotating, but the negative 1 is subtracting the area between the y-axis and the shaded region, so that when it's flipped around, it becomes a washer.

$V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=\pi \cdot \int _1^3\left(1+\frac{2}{y}\right)^2-1dy\\\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\= \pi \left(\int _1^3\left(1+\frac{2}{y}\right)^2dy-\int _1^31dy\right)\\\\$

$\int _1^3\left(1+\frac{2}{y}\right)^2dy=4\ln \left(3\right)+\frac{14}{3}, \int _1^31dy=2\\\\=> \pi \left(4\ln \left(3\right)+\frac{14}{3}-2\right)\\=> \pi \left(4\ln \left(3\right)+\frac{8}{3}\right)$

Our exact solution will be V = π(4In(3) + 8/3). In decimal form it will be about 22.2 however. Try both solution if you like, but it would be better to use 22.2. Your graph will just be a plot under the curve y = 2/x, the first graph.

5 0

3 years ago

The length of a rectangle is four times its width. If the perimeter of the rectangle is 20 feet, how many feet long is the recta

Gemiola [76]

Largeur = x
longueur = 4 x

2 ( x + 4 x) = 20
2 x + 8 x = 20
10 x =20
x = 2

largeur = 2 et longueur = 8

8 0

3 years ago

Please help meeeeeeeeeeeeeeeee

Reika [66]

Answer: tough one

Step-by-step explanation:

7 0

3 years ago